A Framework for Covariate-Adjusted Bivariate Causal Discovery

TL;DR

This paper introduces a nonparametric framework for covariate-adjusted bivariate causal discovery, addressing real-world complexities and providing robust estimation and uncertainty quantification methods, with applications in collider detection and epigenetic studies.

Contribution

It presents a novel, nonparametric approach with a conditional asymmetry coefficient for covariate-adjusted causal inference, improving robustness and applicability over existing methods.

Findings

Superior performance in simulation studies

Effective collider detection in causal structure learning

Successful application to epigenetic data

Abstract

Ascertaining causal direction from observational data is a fundamental challenge in scientific inquiry. Of particular interest is the problem of covariate-adjusted bivariate causal discovery, i.e., determining the causal direction between X and Y in the presence of Z. While unadjusted bivariate causal discovery has seen significant advances (Hoyer et al., 2008; Ni, 2022), there is a lack of methodology dealing with real-world bivariate relationships, which are often modulated by a set of covariate(s), Z. Building on previous work in Purkayastha and Song (2025), we introduce a novel, nonparametric framework for the covariate-adjusted bivariate causal discovery problem and propose a conditional asymmetry coefficient to track said direction of causation. We develop a robust estimation procedure using kernel-based conditional density estimation with cross-fitting and also provide rigorous uncertainty quantification using a nonparametric kernel smoothing technique, addressing a key limitation of many existing algorithms. As a key application, we demonstrate how this framework can be applied to the problem of collider detection, a persistent challenge in causal structure learning. Simulation studies show our method's superior performance in identifying causal structures. We apply our approach to an epigenetic study (Perng et al., 2019), investigating the role of blood pressure in regulating the effects of DNA methylation. In summary, our work offers methodological advancement by providing a robust, inferential toolkit for dissecting complex, moderated bivariate causal relationships in observational data.